Question

find a radical equation of the form sqrt(ax+b)=x+c so that one solution is extraneous

Answer 1

okay. give an example of square root of a number.

Answer 2

4

Answer 3

okay so 4 is the square root of 16.
so ax+b =16
and x+c = 4.

Answer 4

say x is 3, then c is 1.
and 3a+b is 16.
lets say a is 4, then b is also 4.

Answer 5

so your equation could be sqrt(4x+4)=x+1

Answer 6

to find x, square both sides. and post what you got.

Answer 7

-x^2+4x+3=0

Answer 8

x=-1,-3

Answer 9

wait. what is (x+1)^2?

Answer 10

x^2+1

Answer 11

(a+b)^2 is a^2+b^2? are you sure about that?

Answer 12

its 4x+4=x^2+1^2

Answer 13

do you know the formula for \[(a+b)^{2} \]

Answer 14

okay, if you don't know the formula, you can tell me. I will explain.

Answer 15

wait i no this
its 4x+4=x^2+2x+1

Answer 16

yes! solve that expression then.

Answer 17

(x=-1,3)

Answer 18

y, plug in x = 3 and x = -1 in your original expression, sqrt(4x+4)=x+1

Answer 19

oh wait. this is a bad example.

Answer 20

well, anyway, you get the idea. you have to follow the procedure I outlines, such that the original expression is solve by one value of x and the square expression is solved by 2 values of x, giving you one spurious value of x.